LED (Light Emitting Diode) has advantages of small size, long lifetime, low power consumption, and high light efficiency. With the development of various colors of LEDs, LED has extensively replaced traditional light sources and has been widely used in many illumination and display applications. Therefore, many semiconductor manufacturers pay their attention to the development of LED. Similar to a general diode, LED also has forward bias and reverse bias in electric operation. In forward bias, current can easily pass through LED; in reverse bias, almost none current pass through LED. Only forward bias can make LED emit light. Thus, only the positive semi-period of alternating current can drive LED to work. However, LED has a smaller reverse breakdown voltage than general diodes, and the negative semi-period of alternating current can easily puncture LED and may externally damage LED. Therefore, LED needs a special driving circuit, preferably a constant-current driving circuit. Taiwan patent No. M298538 disclosed a “Control Device for LED Vehicle Light”, which comprises: a boost rectifier circuit, a driving IC and a plurality of LED lights. The driving IC controls the boost rectifier circuit and determines the current passing through LED lights. In the prior art, the LED lights are cascaded in the same direction, and the driving IC provides pulse signals to control the boost rectifier circuit to perform a switching type boosting, wherein the current is fluctuating and has a higher point and a lower point. Before reaching the higher point, the current has a stage unable to turn on LED. Further, the driving IC needs a circuit providing a constant voltage. Besides, the driving IC raises the cost of the LED light system. Therefore, the prior art is expensive but has an imperfect performance. Taiwan patent No. I273536 disclosed a “Light Source Circuit, Transformer Circuit, Light-Emitting Panel and Current Balance Method”, wherein several sets of balancing transformers provide several balanced AC powers, and full-wave rectifier circuits transform the AC powers into fluctuating DC powers driving several sets of LED strings. However, the prior art has the disadvantages of non-constant current and high prices because it adopts full-wave rectification and uses at least one transformer. In conclusion, the conventional LED driving circuits still have the problems of non-constant current (fluctuating current) and high prices to overcome.